Big idea Negative numbers help us to model many real world situations. Notes from class -
Positive+Positive=Positive Positive+Negative=Negative
Negative+Negative=Negative Negative+Negative+Positive=Negative So if there are odd numbers of negatives in a number sentence, the answer would be a negative number, and if there are even number of negatives the answer would be positive.
Question: Play the game with a partner. Look for interesting patterns and ideas that might help you devise a winning strategy. Make notes of your observation.
The integer product game
1
-1
2
-2
3
-3
4
-4
5
-5
6
-6
8
-8
9
-9
10
-10
12
-12
15
-15
16
-16
18
-18
20
-20
24
-24
25
-25
30
-30
36
-36
Factors -
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 Game rules -
1.Player A puts a paper clip on a number in a factor list. Player A does not cover a square on the product grid because only one factor has been marked; it takes 2 factors to make a product.
2. Player B puts the other paper clip on any number in the factor list (including the same number marked by Player A) and then shades or covers the product of the 2 factors on the product grid.
3. Player A moves either one of the paper clips to another number and then shades or covers the new product using a different color from player B.
4. Each player, in turn, moves a paper clip and marks a product. If a product is already marked, the player does not get a mark for that turn. The winner is the first player to mark 4 squares in a row-up and down, across, or diagonally.
ways to win - try to use your opportunity to block your opponent's row or try to get 4 squares in a row.
F.U
1. Give every combination of 2 factors from the factor list that will give each of the following products.
a. 5: 5X1, -1X(-5)
b. -12: 1X-12, -1X12, -2X6, 3X-4
c. 12: 12X1, -12X-1, 2X6, -2X-6, -3X-4, 3X4
d. -25: 1X-25, 5X-5 2. Your opponent starts the game by putting a paper clip on -4. What products are possible on your turn?
24, 20, 16, 12, 8, 4, -4, -8, -12, -16, -20, -24 3. At the end of your opponent's turn, the paper clips are on -5 and -2. What move would you make to get a product of -15?
-5X3 4. At the end of your opponent's turn, the paper clips are on -3 and -2. What move would you make to get a product of 6?
-3X-2, -2X-3 5. Why doesn't -35 appear on the board?
It is because there are no 2 factors multiplied and get a -35. If there should be one, the available factors should have a 7 or -7 to get a -35
Summary:
even number of negative numbers would result a positive number and odd number of negative numbers in a number sentence would result a negative number.
4/26/10
4.3 Playing the Integer Product Game
Big idea
Negative numbers help us to model many real world situations.
Notes from class -
Positive+Positive=Positive
Positive+Negative=Negative
Negative+Negative=Negative
Negative+Negative+Positive=Negative
So if there are odd numbers of negatives in a number sentence, the answer would be a negative number, and if there are even number of negatives the answer would be positive.
Question: Play the game with a partner. Look for interesting patterns and ideas that might help you devise a winning strategy. Make notes of your observation.
The integer product game
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Game rules -
1.Player A puts a paper clip on a number in a factor list. Player A does not cover a square on the product grid because only one factor has been marked; it takes 2 factors to make a product.
2. Player B puts the other paper clip on any number in the factor list (including the same number marked by Player A) and then shades or covers the product of the 2 factors on the product grid.
3. Player A moves either one of the paper clips to another number and then shades or covers the new product using a different color from player B.
4. Each player, in turn, moves a paper clip and marks a product. If a product is already marked, the player does not get a mark for that turn. The winner is the first player to mark 4 squares in a row-up and down, across, or diagonally.
ways to win - try to use your opportunity to block your opponent's row or try to get 4 squares in a row.
F.U
1. Give every combination of 2 factors from the factor list that will give each of the following products.
a. 5: 5X1, -1X(-5)
b. -12: 1X-12, -1X12, -2X6, 3X-4
c. 12: 12X1, -12X-1, 2X6, -2X-6, -3X-4, 3X4
d. -25: 1X-25, 5X-5
2. Your opponent starts the game by putting a paper clip on -4. What products are possible on your turn?
24, 20, 16, 12, 8, 4, -4, -8, -12, -16, -20, -24
3. At the end of your opponent's turn, the paper clips are on -5 and -2. What move would you make to get a product of -15?
-5X3
4. At the end of your opponent's turn, the paper clips are on -3 and -2. What move would you make to get a product of 6?
-3X-2, -2X-3
5. Why doesn't -35 appear on the board?
It is because there are no 2 factors multiplied and get a -35. If there should be one, the available factors should have a 7 or -7 to get a -35
Summary:
even number of negative numbers would result a positive number and odd number of negative numbers in a number sentence would result a negative number.